Whisk 2 tbsp olive oil, 2 tbsp lemon juice, 1 tsp lemon zest, 1 tsp Dijon, 1 tbsp minced shallot, 1/4 tsp salt, and a few grinds of pepper in a small bowl. Set it aside so the shallot softens in the lemon juice.

Snap the woody ends off the asparagus by bending each spear until it breaks, then toss the spears with 1 tbsp olive oil and 1/8 tsp salt. In a separate bowl, toss the torn bread with 1 tbsp olive oil and 1/8 tsp salt.

Pour about 4 cm / 1.5 inches of water into a 26 cm / 10-inch deep skillet, add 1 tbsp white vinegar, and bring it to a bare simmer over medium-low heat.

Heat a 30 cm / 12-inch cast-iron skillet over medium heat for 2 minutes. Add the bread and cook for 4 minutes, stirring often, until golden and crisp at the edges. Tip the croutons onto a plate.

Raise the heat to medium-high. Lay half the asparagus in a single layer and cook for 5 minutes, turning every 1 to 2 minutes, until dark blistered spots show and the spears are bright green with a little spring left. Move them to a board and repeat with the second half.

When the second batch has been charring for about 2 minutes, lower the poaching water to small, lazy bubbles. Crack each egg into a ramekin and slide it in at the edge of the pan. Poach for 3 minutes, until the whites are set and the yolks still wobble. If the water boils hard, the whites shred into wisps, so lower the heat right away. Lift the eggs out with a slotted spoon and touch them to a paper towel.

Toss the arugula with half the dressing and divide it between two plates. Arrange the asparagus on top, scatter over the croutons and shaved Parmesan, and set 2 eggs on each plate. Spoon over the remaining dressing, then finish with flaky salt, pepper, and chives. Serve right away.